Post by Sapphire Capital on Jul 11, 2008 7:11:54 GMT 4
Optimal Static-Dynamic Hedges for Exotic Options under Convex Risk Measures
AYTAC ILHAN
University of Oxford - Mathematical Institute
MATTIAS JONSSON
University of Michigan at Ann Arbor - Department of Mathematics
RONNIE SIRCAR
Princeton University - Department of Operations Research and Financial Engineering
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April 8, 2008
Abstract:
We study the problem of optimally hedging exotic derivatives positions using a combination of dynamic trading strategies in underlying stocks, and static positions in vanilla options when the performance is quantified by a convex risk measure. We establish conditions for the existence of an optimal static position for general convex risk measures, and then analyze in detail the case of expected shortfall with a power loss function. Here we find conditions for uniqueness of the static hedge. We illustrate the computational challenge of computing the market-adjusted risk measure in a simple diffusion model for an option on a non-traded asset.
papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1121233_code338319.pdf?abstractid=1121233&mirid=1
AYTAC ILHAN
University of Oxford - Mathematical Institute
MATTIAS JONSSON
University of Michigan at Ann Arbor - Department of Mathematics
RONNIE SIRCAR
Princeton University - Department of Operations Research and Financial Engineering
--------------------------------------------------------------------------------
April 8, 2008
Abstract:
We study the problem of optimally hedging exotic derivatives positions using a combination of dynamic trading strategies in underlying stocks, and static positions in vanilla options when the performance is quantified by a convex risk measure. We establish conditions for the existence of an optimal static position for general convex risk measures, and then analyze in detail the case of expected shortfall with a power loss function. Here we find conditions for uniqueness of the static hedge. We illustrate the computational challenge of computing the market-adjusted risk measure in a simple diffusion model for an option on a non-traded asset.
papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1121233_code338319.pdf?abstractid=1121233&mirid=1